The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.